editing disabled

Division of a sixth (e. g. 5/3 or 11/7) into n equal parts

Division of e. g. the 5:3 or the 11:7 into equal parts can be conceived of as to directly use this interval as an equivalence, or not. The question of equivalence has not even been posed yet. The utility of 5:3 or 11:7 or another sixth as a base though, is apparent by being named directly in the standard definition of such as the octave based sensi temperament or factoring into chord inversions. Many, though not all, of these scales have a pseudo (false) octave, with various degrees of accuracy, but which context(s), if any, it is very perceptually important in is as yet an open question.

Incidentally, one way to treat 5/3 or 11/7 as an equivalence is the use of the 6:7:8:(10) or 7:8:9:(11) chord as the fundamental complete sonority in a very similar way to the 4:5:6:(8) chord in meantone. Whereas in meantone it takes four 3/2 to get to 5/1, here it takes four 4/3 to get to 8/7 (tempering out the comma 225/224) or four 9/7 to get to 9/8 (tempering out the comma 5929/5832). So, doing this yields 7, 9, and 16 note MOS either way, the 16 note MOS of the two temperaments being mirror images of each other (7L 9s for ed(5/3)s vs 9L 7s for ed(11/7)s). While the notes are rather closer together, the scheme is uncannily similar to meantone. "Microdiatonic" might be a good term for it (even better than for edfs as the generator it uses is an excellent fit for heptatonic MOS) if it hasn't been named yet.